Homotopy Invariants for gradable finite dimensional algebras

TL;DR

This paper demonstrates that for gradable finite dimensional algebras, homotopy invariants cannot differentiate between perfect complexes and the bounded derived category, highlighting limitations in homotopy-based classification.

Contribution

It establishes a fundamental limitation of homotopy invariants in distinguishing certain derived categories of gradable finite dimensional algebras.

Findings

Homotopy invariants fail to distinguish perfect complexes from bounded derived categories in gradable finite dimensional algebras.

The result applies specifically to gradable finite dimensional algebras, indicating a boundary for homotopy invariant effectiveness.

Provides insight into the structure of derived categories and the limitations of homotopy invariants in algebra classification.

Abstract

We show that for a gradable finite dimensional algebra the perfect complexes and bounded derived category cannot be distinguished by homotopy invariants.